Question 1

Which of the following describes the transformation from $$y = f(x) to$$ $$y = f(x) + 3$$?

Accepted Answer

A vertical shift upward by 3 units

Question 2

Given $$y = f(x)$$, what is the effect of the transformation $$y = f(x - 4)$$?

Accepted Answer

Shift the graph 4 units to the right

Question 3

If $$y = f(x) is $$reflected about the x-axis, which equation represents the new graph?

Accepted Answer

$$y = -f(x)$$

Question 4

Which transformation results in a horizontal shrink of the graph of $$y = f(x) by a $$factor of 3?

Accepted Answer

$$y = f(3x)$$

Question 5

Suppose $$y = f(x) is $$vertically stretched by a factor of 2. Which equation represents this transformation?

Accepted Answer

$$y = 2f(x)$$

Question 6

A function $$y = f(x) is $$reflected about the y-axis and then shifted up by 5 units. What is the resulting equation?

Accepted Answer

$$y = f(-x) + 5$$

Question 7

Which sequence of transformations is correct for graphing $$y = -2f(x + 1) - 3$$?

Accepted Answer

Shift left 1, stretch vertically by 2, reflect about x-axis, shift down 3

Question 8

If $$y = f(x) is $$horizontally stretched by a factor of 4, what is the equation of the new graph?

Accepted Answer

$$y = f\left(\frac{1}{4}x\right)$$

Question 9

A real-world scenario: The height $$h (in $$meters) of a bouncing ball at time $$t (in $$seconds) is modeled by $$h(t) = -5(t-2)^2$ + 20. $$Which transformation has been applied to the basic quadratic $$y = -5t^2$?

Accepted Answer

Shifted right 2 units and up 20 units

Question 10

Given $$y = f(x)$$, what is the effect of the transformation $$y = -f(-x)$$?

Accepted Answer

Reflection about both the x-axis and y-axis

Question 11

Which of the following best describes the transformation from $$y = f(x) to$$ $$y = f(x + 2) - 4$$?

Accepted Answer

Shift left 2 units, then down 4 units

Question 12

If $$y = f(x) is $$vertically shrunk by a factor of $$\frac{1}{3}$$, what is the equation of the new graph?

Accepted Answer

$$y = \frac{1}{3}f(x)$$

Question 13

A company’s profit $$P (in $$thousands of dollars) as a function of time $$t (in $$years) is $$P(t) = 2f(0.5t) + 10. $$Which transformations have been applied to $$y = f(t)$$?

Accepted Answer

Vertical stretch by 2, horizontal stretch by 2, up 10 units

Question 14

Which transformation would change the graph of $$y = f(x) to$$ $$y = f(-x) + 7$$?

Accepted Answer

Reflect about the y-axis, then shift up 7 units

Question 15

If $$y = f(x) is $$shifted right by 6 units and then reflected about the x-axis, what is the equation of the new graph?

Accepted Answer

$$y = -f(x - 6)$$

Question 16

Which of the following is the correct order of transformations for $$y = 3f(-2x + 1) - 4$$?

Accepted Answer

Shift left $$\frac{1}{2}$$, horizontal shrink by 2, reflect about y-axis, vertical stretch by 3, shift down 4

Question 17

A medical researcher models the temperature $$T (in$$ °C) of a patient’s body after medication as $$T(t) = 0.8f(2t - 4) + 1. $$Which of the following is NOT a transformation applied to $$y = f(t)$$?

Accepted Answer

Vertical stretch by 2

Question 18

Which transformation would result in the graph of $$y = f(x)$$ being reflected about the x-axis and then shifted down by 2 units?

Accepted Answer

$$y = -f(x) - 2$$

Question 19

If $$y = f(x) is $$horizontally shrunk by a factor of $$\frac{1}{5}$$, what is the equation of the new graph?

Accepted Answer

$$y = f\left(\frac{1}{5}x\right)$$

Transformations of Functions: Precalculus Study Guide

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